Algebraic decoders may use operations on Galois Field elements to decode error correction codes. The operations typically include determining an inverse or a logarithm of an element, and methods for such determination are known in the art.
For example, U.S. Pat. No. 6,199,088, to Weng et al., whose disclosure is incorporated herein by reference, describes a circuit for determining multiplicative inverses in certain Galois Fields. A division of two elements B/A is performed by producing a multiplicative inverse of A and then multiplying B by A−1.
U.S. Pat. No. 6,279,023, to Weng et al., whose disclosure is incorporated herein by reference, describes a system for computing the multiplicative inverse of an element of a Galois Field without using tables. The system is stated to raise the element to the power 2m−2.
Documents incorporated by reference in the present patent application are to be considered an integral part of the application except that to the extent any terms are defined in these incorporated documents in a manner that conflicts with the definitions made explicitly or implicitly in the present specification, only the definitions in the present specification should be considered.